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Number of nine-lettered word that can be...

Number of nine-lettered word that can be formed using all the letters of the word 'MEENANSHU' if alike letters are never adjacent is

A

`12xx6!`

B

`11*7!`

C

`13*6!`

D

`12*11*6!`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `'MEENASHU'` . Number of letters `=9("EE"=2,"NN"=2)`
`:. "Number of ways" =("Total words formed")-("words in which EE together"+"words in which NN together"-"words in which EE together and NN together")`
`=(9!)/(2!*2!)-[(2*8!)/(2!)-7!]`
`=18*7!-7*7!=(18-7)7!=11*7!`
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